Gu Yonghao, Xu Xin
Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Ministry of Education Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, Shanghai 200433, China.
J Chem Theory Comput. 2021 Dec 14;17(12):7745-7752. doi: 10.1021/acs.jctc.1c00990. Epub 2021 Nov 28.
In electronic structure theory, when an approximate wavefunction tends to artifactually break the symmetry of the exact Hamiltonian, the corresponding method is referred to as having a "symmetry dilemma" problem. Such types of artifacts were often reported when Hartree-Fock (HF) and the low-level post-HF methods were used, while the traditional Kohn-Sham density functional theory (KS-DFT) methods were usually found to be more resistant to this breakdown. In this work, we present a systematic study on the reliability of the doubly hybrid (DH) DFT methods for several violable cases. Almost all the commonly used B2PLYP-type (bDH) functionals are shown to have a severe "symmetry dilemma" problem and yield dramatically unreliable molecular properties, such as dipole moment, vibrational frequency, and static polarizability at the equilibrium geometry. A one-parameter bDH functional model study demonstrates that such a problem is a combined effect of the inappropriate portion of the HF exchange (over 50%) for the self-consistent field (SCF) calculation and the augmentation of the second-order perturbative contribution. It is remarkable that the XYG3-type (xDH) functionals show a good capability to resist the artifactual symmetry breaking and yield reliable molecular properties when the same critical cases are calculated. In the xDH, there are two functionals of different purposes, namely, the SCF functional and the energy functional, which have different amounts of the HF exchange and different portions of the correlation contributions. The success of the xDHs can be attributed to this flexibility in xDH construction to avoid using an improperly large portion of the HF exchange in the SCF functional. The insights gained in this work are of significance for the development of an improved DH functional.
在电子结构理论中，当一个近似波函数倾向于人为地破坏精确哈密顿量的对称性时，相应的方法被称为存在“对称性困境”问题。当使用哈特里 - 福克（HF）和低水平的后HF方法时，经常会报道这类人为现象，而传统的科恩 - 沙姆密度泛函理论（KS - DFT）方法通常被发现对这种对称性破坏具有更强的抵抗力。在这项工作中，我们针对几个可能出现问题的情况，对双杂化（DH）DFT方法的可靠性进行了系统研究。几乎所有常用的B2PLYP型（bDH）泛函都显示出存在严重的“对称性困境”问题，并产生极其不可靠的分子性质，如平衡几何结构下的偶极矩、振动频率和静态极化率。一个单参数bDH泛函模型研究表明，这样的问题是自洽场（SCF）计算中HF交换（超过50%）的不适当部分与二阶微扰贡献增加的综合效应。值得注意的是，当计算相同的关键情况时，XYG3型（xDH）泛函显示出良好的抵抗人为对称性破坏的能力，并产生可靠的分子性质。在xDH中，有两种不同用途的泛函，即SCF泛函和能量泛函，它们具有不同数量的HF交换和不同比例的相关贡献。xDH的成功可归因于其构建过程中的这种灵活性，从而避免在SCF泛函中使用过大比例的HF交换。这项工作中获得的见解对于改进DH泛函的开发具有重要意义。
